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A C# Implementation of Douglas-Peucker Line Approximation Algorithm

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6 Jun 2007MIT 154.8K   3.5K   60   39
DP Line approximation algorithm is a well-known method to approximate 2D lines. It is quite fast, O(nlog_2(n)) for a n-points line and can drastically compress a data curve. Here, a fully OOP implementation is given.

Introduction

I have found multiple implementations of the Douglas-Peucker algorithm but not in any .NET language, so I decided to port it over. Jonathan de Halleux has a wonderful explanation here.

Background

I needed to reduce polygons size to display on a map based on zoom levels.

Using the Code

The code included is complete and should run out of the box in Visual Studio 2005. If it does not, please let me know.

C#
/// <summary>
/// Uses the Douglas Peucker algorithm to reduce the number of points.
/// </summary>
/// <param name="Points">The points.</param>
/// <param name="Tolerance">The tolerance.</param>
/// <returns></returns>
public static List<Point> DouglasPeuckerReduction
    (List<Point> Points, Double Tolerance)
{
    if (Points == null || Points.Count < 3)
    return Points;

    Int32 firstPoint = 0;
    Int32 lastPoint = Points.Count - 1;
    List<Int32> pointIndexsToKeep = new List<Int32>();

    //Add the first and last index to the keepers
    pointIndexsToKeep.Add(firstPoint);
    pointIndexsToKeep.Add(lastPoint);

    //The first and the last point cannot be the same
    while (Points[firstPoint].Equals(Points[lastPoint]))
    {
        lastPoint--;
    }

    DouglasPeuckerReduction(Points, firstPoint, lastPoint, 
    Tolerance, ref pointIndexsToKeep);

    List<Point> returnPoints = new List<Point>();
    pointIndexsToKeep.Sort();
    foreach (Int32 index in pointIndexsToKeep)
    {
        returnPoints.Add(Points[index]);
    }

    return returnPoints;
}
    
/// <summary>
/// Douglases the peucker reduction.
/// </summary>
/// <param name="points">The points.</param>
/// <param name="firstPoint">The first point.</param>
/// <param name="lastPoint">The last point.</param>
/// <param name="tolerance">The tolerance.</param>
/// <param name="pointIndexsToKeep">The point index to keep.</param>
private static void DouglasPeuckerReduction(List<Point> 
    points, Int32 firstPoint, Int32 lastPoint, Double tolerance, 
    ref List<Int32> pointIndexsToKeep)
{
    Double maxDistance = 0;
    Int32 indexFarthest = 0;
    
    for (Int32 index = firstPoint; index < lastPoint; index++)
    {
        Double distance = PerpendicularDistance
            (points[firstPoint], points[lastPoint], points[index]);
        if (distance > maxDistance)
        {
            maxDistance = distance;
            indexFarthest = index;
        }
    }

    if (maxDistance > tolerance && indexFarthest != 0)
    {
        //Add the largest point that exceeds the tolerance
        pointIndexsToKeep.Add(indexFarthest);
    
        DouglasPeuckerReduction(points, firstPoint, 
        indexFarthest, tolerance, ref pointIndexsToKeep);
        DouglasPeuckerReduction(points, indexFarthest, 
        lastPoint, tolerance, ref pointIndexsToKeep);
    }
}

/// <summary>
/// The distance of a point from a line made from point1 and point2.
/// </summary>
/// <param name="pt1">The PT1.</param>
/// <param name="pt2">The PT2.</param>
/// <param name="p">The p.</param>
/// <returns></returns>
public static Double PerpendicularDistance
    (Point Point1, Point Point2, Point Point)
{
    //Area = |(1/2)(x1y2 + x2y3 + x3y1 - x2y1 - x3y2 - x1y3)|   *Area of triangle
    //Base = v((x1-x2)²+(x1-x2)²)                               *Base of Triangle*
    //Area = .5*Base*H                                          *Solve for height
    //Height = Area/.5/Base

    Double area = Math.Abs(.5 * (Point1.X * Point2.Y + Point2.X * 
    Point.Y + Point.X * Point1.Y - Point2.X * Point1.Y - Point.X * 
    Point2.Y - Point1.X * Point.Y));
    Double bottom = Math.Sqrt(Math.Pow(Point1.X - Point2.X, 2) + 
    Math.Pow(Point1.Y - Point2.Y, 2));
    Double height = area / bottom * 2;

    return height;
    
    //Another option
    //Double A = Point.X - Point1.X;
    //Double B = Point.Y - Point1.Y;
    //Double C = Point2.X - Point1.X;
    //Double D = Point2.Y - Point1.Y;
    
    //Double dot = A * C + B * D;
    //Double len_sq = C * C + D * D;
    //Double param = dot / len_sq;
    
    //Double xx, yy;
    
    //if (param < 0)
    //{
    //    xx = Point1.X;
    //    yy = Point1.Y;
    //}
    //else if (param > 1)
    //{
    //    xx = Point2.X;
    //    yy = Point2.Y;
    //}
    //else
    //{
    //    xx = Point1.X + param * C;
    //    yy = Point1.Y + param * D;
    //}
    
    //Double d = DistanceBetweenOn2DPlane(Point, new Point(xx, yy));
}

Points of Interest

The code is not overly complicated. It was fun to port this algorithm, since all I feel I do nowadays is hold business' hands to help them try and solve business problems that there is no consensus on.

History

  • Beta 1

License

This article, along with any associated source code and files, is licensed under The MIT License


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Comments and Discussions

 
QuestionMore efficient version in Loyc.Math + Bug fix Pin
Qwertie22-Nov-23 10:03
Qwertie22-Nov-23 10:03 
QuestionAddition to get rid of possible StackOverflow Exception Pin
Alexander Panfilenok12-Oct-23 5:08
Alexander Panfilenok12-Oct-23 5:08 
QuestionThanks! Pin
Keith Rule21-May-22 9:19
professionalKeith Rule21-May-22 9:19 
Questionrejecting recursion + distance calc acceleration Pin
adevder19-Feb-17 0:12
adevder19-Feb-17 0:12 
AnswerRe: rejecting recursion + distance calc acceleration Pin
TerrySpiderman21-Mar-17 3:05
professionalTerrySpiderman21-Mar-17 3:05 
Questionto save stack memory with great amount of points and tolerance near zero i prefer to reject recursion Pin
adevder18-Feb-17 1:22
adevder18-Feb-17 1:22 
PraiseNice Pin
veen_rp18-Apr-16 19:41
professionalveen_rp18-Apr-16 19:41 
BugIf (first = last) Bug! Pin
Giovani Luigi14-Dec-15 12:44
Giovani Luigi14-Dec-15 12:44 
GeneralRe: If (first = last) Bug! Pin
Keith Rule21-May-22 13:40
professionalKeith Rule21-May-22 13:40 
Thanks for this comment. It saved me from having to troubleshoot that weird last point being off in some random direction issue. This fix solved the problem. Thanks for saving me a bunch of troubleshooting.
Keith Rule

QuestionDouglasPeuckerN() conversion? Pin
cbordeman11-Dec-15 17:42
cbordeman11-Dec-15 17:42 
AnswerRe: DouglasPeuckerN() conversion? Pin
Mr Lorenz27-Apr-17 7:44
Mr Lorenz27-Apr-17 7:44 
GeneralUseful Pin
Dineshkumar_MCA22-Apr-15 2:18
professionalDineshkumar_MCA22-Apr-15 2:18 
QuestionBUG tolerance Pin
Member 1017584518-Feb-15 2:08
Member 1017584518-Feb-15 2:08 
QuestionThanks + pruned code Pin
Stoyan Haralampiev23-Oct-14 3:30
Stoyan Haralampiev23-Oct-14 3:30 
QuestionUsing this algorithm on data from database Pin
Saket Surya2-Jun-14 3:38
Saket Surya2-Jun-14 3:38 
QuestionPoint projected on the line but behind the segment? Bug? Pin
Sergiy Tkachuk25-Mar-14 14:31
Sergiy Tkachuk25-Mar-14 14:31 
QuestionAbout Tolerance Pin
kamlesh Prajapati8-Jan-14 23:55
kamlesh Prajapati8-Jan-14 23:55 
QuestionWhy do you create your own Point? Pin
leiyangge3-Jan-14 22:37
leiyangge3-Jan-14 22:37 
QuestionLicense Pin
Diego Catalano14-Dec-13 2:42
Diego Catalano14-Dec-13 2:42 
Question1 bug, + 1 potential bug Pin
gyuri1023-Apr-12 23:45
gyuri1023-Apr-12 23:45 
AnswerRe: 1 bug, + 1 potential bug Pin
tplokas26-Mar-13 14:46
tplokas26-Mar-13 14:46 
QuestionUseful,Thanks! Pin
masy19112-Mar-12 23:43
masy19112-Mar-12 23:43 
QuestionGreat Job! Pin
Christopher Drake19-Dec-11 8:32
Christopher Drake19-Dec-11 8:32 
Generalhow calculate an epsilon value Pin
unravel-the-sky23-May-11 6:52
unravel-the-sky23-May-11 6:52 
GeneralSome Issues with your implementation Pin
MattMi15-Jul-10 11:57
MattMi15-Jul-10 11:57 

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